Let F be a boolean formula. A
statement of a the form "There exists an assignment that sets F to TRUE" has a
short proof. Such a proof is simply an assignment that sets F to TRUE. The
complimenting statement, which is of the form "All assignments set F to FALSE"
seems much harder to prove. In this course we shall study the complexity of
proving such universal statements and address the following questions:

What is a proof?

How long can a proof be as a function of the length of the statement?

If a short proof exists, can we find it?

Are statements about computation hard to prove?

How does all this relate to the fundamental question of P vs. NP (and
NP vs. coNP)?